Crosstalk (or inter-channel interference) is a major source of channel impairment for wired communication systems, such as Digital subscriber Line (xDSL) communication systems.
As the demand for higher data rates increases, systems are evolving toward higher frequency bands, wherein crosstalk between neighboring transmission lines (that is to say transmission lines that are in close vicinity over part or whole of their length, such as twisted copper pairs in a cable binder) is more pronounced (the higher frequency, the more coupling).
For instance, in the recommendation entitled “Very High Speed Digital subscriber Line Transceivers 2”, ref. G.993.2, and adopted by the International Telecommunication union (ITU) in April 2010 (VDSL2 hereinafter), the transmit spectrum has been broadened from 2,208 MHz (ADSL2+) up to 17,664 MHz with transmit profile 17a and 4,3125 kHz tone spacing. In G.9701 ITU recommendation (G.fast hereinafter), the transmit spectrum goes up to 105,93225 MHz with transmit profiles 106a or 106b and 51.75 kHz tone spacing.
Different strategies have been developed to mitigate crosstalk and to maximize effective throughput, reach and line stability. These techniques are gradually evolving from static or dynamic spectrum management techniques to multi-user signal coordination a.k.a. vectoring.
One vectoring technique for mitigating crosstalk is signal precoding: the user data symbols are jointly passed through a precoder before being transmitted over the respective communication channels. The precoder is such that the concatenation of the precoder and the communication channels results in little or no inter-channel interference at the receivers.
A further vectoring technique for mitigating crosstalk is signal postcoding (or post-processing): the receive data symbols are jointly passed through a postcoder (a.k.a. crosstalk cancellation filter) before being detected. The postcoder is such that the concatenation of the communication channels and the postcoder results in little or no inter-channel interference at the detectors.
Signal vectoring is typically performed at a traffic aggregation point as multi-user signal coordination between co-located transceivers is required: signal precoding is particularly appropriate for downstream communication (i.e., toward customer premises), while signal postcoding is particularly appropriate for upstream communication (i.e., from customer premises).
More formally, an N×N Multiple Input Multiple output (MIMO) channel can be described by the following linear model:yk=Hkxk+zk  (1),wherein the N-component complex vector xk, respectively yk, is a discrete frequency representation, as a function of the frequency index k, of the symbols transmitted over, respectively received from, the N vectored channels,wherein the N×N complex matrix Hk is the channel matrix: the (i,j)-th component Hi,j of the channel matrix Hk describes how the communication system produces a signal on the i-th channel output in response to a signal being fed to the j-th channel input; the diagonal elements of the channel matrix describe direct channel coupling, and the off-diagonal elements of the channel matrix (also referred to as the crosstalk coefficients) describe inter-channel coupling,and wherein the N-component complex vector zk denotes additive noise over the N channels, such as Radio Frequency Interference (RFI) or thermal noise.
Signal precoding and postcoding are advantageously implemented by means of matrix products.
In downstream, a linear precoder performs a matrix-product in the frequency domain of a data vector uk with a precoding matrix Pk before actual transmission over the respective communication channels, i.e. actual transmit vector is xk=Pkuk.
In upstream, a linear postcoder performs a matrix-product in the frequency domain of the receive vector yk with a postcoding matrix Qk to recover the data vector uk (after channel equalization and power normalization), i.e. detection is performed on y′k=Qkyk.
In order to leverage on the expected vectoring gains, the ITU has recently proposed a new VDSL2 transmit profile to provide even higher data rates on short loops. VDSL2 35b transmit profile (a.k.a. vplus) extends 17a transmit profile up to 35,328 MHz while sticking to the same 4,3125 kHz tone spacing, thus doubling the number of available tones from 4096 to 8192. A similar extended transmit profile 212a, which extends 106a/b transmit profile from 105,93225 MHz up to 211,8645 MHz, has been defined for G.fast.
Consequently, one may expect that both VDSL2 17a and 35b transmit profiles will coexist over the same copper plant, and so probably will G.fast 106a/b and 212a transmit profiles. The co-existence of different transmit profiles within a common loop plant may bring about some additional crosstalk that ultimately translates into lower-than-expected data rates.
Indeed, the sampling frequency is typically configured as twice the upper bound of the broadest supported transmit profile (as dictated by Nyquist Shannon theorem). Presently, legacy equipment supporting 17a transmit profile are likely to use 35,328 MHz as sampling frequency for synthesizing the transmit outgoing signal from the IFFT samples or for sampling the receive incoming signal, while equipment supporting new 35b transmit profile are likely to use 70,656 MHz as sampling frequency.
This additional crosstalk is twofold. A first source of crosstalk is caused by the synthesis of the transmit analog signal over the legacy 17a lines with 35,328 MHz as sampling frequency: part of the original transmit spectrum is mirrored with respect to the shannon frequency (aka folding frequency, i.e. half the sampling frequency) into the first alias band spanning from 17,664 MHz up to 35,328 MHz, which mirrored signal then interfering with the useful communication signals on the 35b lines. A second source of crosstalk is caused by the sampling of the receive analog signal over the legacy 17a lines with 35,328 MHz as sampling frequency: communications over the 35b lines causes crosstalk in the first alias band of the legacy 17a lines, and these crosstalk signals are then mirrored back into the 17a communication band after signal sampling. This additional crosstalk can be partly mitigated by the use of appropriate transmit smoothing filters and receive anti-alias filters. Even then, and due to imperfect filtering (cheap low-order filters are typically used at subscriber side), the impairment is still particularly significant for the upper tones nearby the folding frequency, and may completely annihilate the expected vectoring gains for those tones.
This issue has been acknowledged by British Telecom for mixed VDSL2 17a/35b deployments in the contribution entitled “On vectoring with mixed order Fourier transforms” published by the ITU in November 2015 with ref. 2015-11-Q4-049R1, and for mixed G.fast 106a/212a deployments in the contribution entitled “G. fast: On vector groups with multiple sampling frequencies” published by the ITU in April 2016 with ref. 2016-04-Q4-042.
There is seen in FIG. 1 two plots 1 and 2 in logarithmic scale of the applicable transmit Power Spectral Density (PSD) masks over a 106a and 212a line respectively around the folding frequency fk=105,93225 MHz. The actual transmit signal PSD over the 106a line has been depicted as plot 3. As one can notice, the alias transmit signal above 106 MHz starts being filtered. The ‘virtual’ transmit noise floors 4 and 5 are depicted for two typical loop lengths (receive background noise times the inverse of the direct path loss). The difference between the curves 3 and 4 or 3 and 5 (plus some noise margin) represents the possible vectoring gains over the 106a line (see arrow in FIG. 1).
As one can see a substantial amount of the alias signal over the 106a line just above the folding frequency fK can leak into the 212a line and affect the upper tones nearby the folding frequency. As an illustration, the expected alias crosstalk for the 212a line has been depicted as plot 6 in FIG. 1. This alias crosstalk adds up to the background noise floor 3 or 4, and could possibly annihilate all possible vectoring gains over the corresponding tones. Likewise, a substantial amount of the transmit signal over the 212a lines above the folding frequency fK can leak into the 106a lines, be aliased back and affect the lower tones nearby the folding frequency fK (not shown).
As a first partial solution to this problem, one could re-connect all legacy 17a lines to 35b-capable transceivers at the access node, meaning that downstream transmit and upstream receive 17a signals would be over-sampled at 70,656 MHz. Yet, upstream communications over the 35b lines would still suffer from the alias interference caused by non-oversampled 17a customer Premises Equipment (CPE). Also, such a line re-dispatching would cause service disruption, and would substantially increase the CAPital and OPerational EXpenditures (CAPEX and OPEX) on account of the necessary equipment upgrade and deployment of maintenance staff on the field.
Another way to solve this problems is to switch off some tones above and nearby 17,664 MHz for the 35b lines such that they cannot get affected and such that they don't affect lower tones on 17a lines. However, this solution results in substantial data rate loss.
Some proposals have been made to cancel this additional crosstalk in the vectoring Processor (VP). Current VPs are typically fed with frequency samples in increasing tone order, which means that you need a buffer for each line to remember all tones data below the folding frequency till the tone data above the folding frequency start being fed to the VP. Not only such a solution requires large buffer memory in the VP, which induces a substantial additional cost for the VP, but it also introduces large latency in the data path.